New Stability Criteria of Delayed Load Frequency Control Systems via Infinite-Series-Based Inequality

Yang, Feisheng; He, Jing; Wang, Dianhui

doi:10.1109/tii.2017.2751510

Cited by 85 publications

(46 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…During the development of the above criterion, two relaxed conditions are obtained by combing the auxiliary function inequality and the reciprocally convex lemma and constructing a new augmented Lyapunov functional and they makes the criterion be less conservative than the one reported in [23], which will be illustrated in the next section.…”

Section: Remarkmentioning

confidence: 99%

“…In this section, for one-area and two-area power systems, case studies are given to investigate the application and effectiveness of the proposed method and to show the improvement of the proposed criterion than the one reported in previous publications. The parameters concerned are recalled from [23] and listed in Table 1.…”

Section: Case Studiesmentioning

confidence: 99%

“…For different gains of PI controller (K P changed in the range of [0, 1.0], K I changed in the range of [0.05, 1.0]) and two types of delays (i.e., constant delays µ = 0, time-varying delays µ = 0.9), the stability margins are calculated via the method proposed and listed in Tables 2 and 3. Moreover, the results reported in [14,20,23] are also given for comparison to account for the superiority of the method proposed.…”

Section: The Case Of a One-area Systemmentioning

confidence: 99%

“…More specifically, the criteria developed are used to understand the influence of the delay on the stability of the LFC systems and to obtain the delay stability region, which is an allowable region of time-varying delay that the LFC system can tolerate. However, the methods for developing the above criteria, even the best one in [23], are still conservative so as to lead to conservative results, which may make a requirement of the communication network more strict than its indeed needs. Therefore, in order to increase the accuracy of the delay stability region found, how to derive a stability criterion with less conservatism needs further investigation.…”

mentioning

confidence: 99%

See 3 more Smart Citations

An Improved Stability Criterion for Load Frequency Control of Power Systems with Time-Varying Delays

et al. 2020

View full text Add to dashboard Cite

This paper aims at developing a novel stability criterion to access the influence of the time-varying delay on the stability of power systems equipped with a proportional-integral (PI)-based load frequency control (LFC). The model of the LFC scheme considering time-varying communication delays is established at first. Then, an improved stability condition related to the information of delay bounds is deduced by constructing an augmented Lyapunov-Krasovski functional and using a matrix inequality, and it is expressed as linear matrix inequalities (LMIs) for easily checking. Finally, case studies for one-area and two-area LFC systems are carried out to show the relationship between delay margins ensuring the stability and the PI gains of the LFC, and also verify the superiority of proposed stability criterion compared with the previous ones.Energies 2020, 13, 2101 2 of 14 regular polynomial [11]. Furthermore, the method proposed in [12] realized the elimination process of transforming the transcendental characteristic equation into the cross frequency standard polynomial. The frequency-domain method can acquire accurate stability margins under the case of constant delays, while it cannot process the case of time-varying delays and has certain limitations. For the time-varying delays, the time-domain method based on the Lyapunov stability theory is more available.The delay margin of the traditional multi-area LFC scheme [14] and the deregulated market environment [15] as well as the relationship between the delay margin and the proportional-integral (PI) gain were discussed. However, since the stability analysis that produces these standards rely on a large number of free weighted matrix variables, the amount of calculation is huge. In [5,16], by taking into account both the random delays and the data packet, the stability of LFC scheme was discussed, but they did not put forward any way based on the delay stability margin to estimate the performance of the control system. In order to obtain more accurate stability margins, the delay correlation stability for a deregulated LFC system with probabilistic interval delays [17] or two additive time-varying delays [18] were analyzed through developing less conservative stability criteria. In [19], for the multi-area power systems, the exponential stability problem was investigated based on a transformed switching system with multiple time delays. By modeling the load disturbances as bounded perturbations, the authors in [20] analyzed the delay-and disturbance-dependent stability of the LFC system. Moreover, several stability criteria established via the double integral inequality in the form of auxiliary function [21], the truncated B-L inequality [22], and improved integral inequality [23] were used to improve the results.Although the aforementioned criteria were developed via different methods, the existing research results still have room for improvement. More specifically, the criteria developed are used to understand the influence of the delay on the stability of the...

show abstract

Section: Remarkmentioning

confidence: 99%

Section: Case Studiesmentioning

confidence: 99%

Section: The Case Of a One-area Systemmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

An Improved Stability Criterion for Load Frequency Control of Power Systems with Time-Varying Delays

et al. 2020

View full text Add to dashboard Cite

show abstract

“…x It is expected that this B-L inequality will play an important part in conservatism reduction of stability conditions on systems with interval time-varying delay. Specifically, second-order B-L inequality recovers the truncated infinite-series-based inequality, 48 which was successfully applied to load frequency control of delayed power systems in our most recent work 49 and the auxiliary function-based single integral inequality in the work of Park et al 17…”

Section: Time-delay System Modelmentioning

confidence: 99%

Delay range‐and‐rate dependent stability criteria for systems with interval time‐varying delay via a quasi‐quadratic convex framework

Yang

Kang

2019

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

Summary This paper concerns the stability analysis of systems with interval time‐varying delay. A Lyapunov‐Krasovskii functional containing an augmented quadratic term and certain triple integral terms is constructed to integrate features of the truncated Bessel‐Legendre inequality less conservative than Wirtinger inequality that encompasses Jensen inequality, respectively, and to exploit merits of the newly developed double integral inequalities tighter than auxiliary function‐based, Wirtinger, and Jensen double integral inequalities. A new quadratic convex lemma is proposed to derive delay and its derivative dependent sufficient stability conditions in terms of linear matrix inequalities synthetically with reciprocal convex approach and affine convex combination. The efficiency of the presented method is illustrated on some classical numerical examples.

show abstract

Robust load frequency control of power systems with two time delays

Tan

Shi

Liu

et al. 2021

Int Trans Electr Energ Syst

View full text Add to dashboard Cite

This paper is concerned with the robust H ∞ load frequency control (LFC) of power systems with two time delays in the presence of load disturbance. Firstly, the original power systems with the proportional-integral (PI)-type LFC are converted into an output feedback control system with two time delays. Secondly, an improved reciprocally convex inequality is proposed, and a less conservative robust H ∞ criterion is derived, which can be used to design the PI-type LFC with robust H ∞ performance. Then, based on the robust H ∞ criterion, an algorithm is provided to obtain the PI-type LFC gain and the time delay margin, which effectively convert the coupled nonlinear terms into linear items without solving the inverse of the matrix with row full rank. Finally, simulations are shown to verify the superiority of the presented method.

show abstract

New Stability Criteria of Delayed Load Frequency Control Systems via Infinite-Series-Based Inequality

Cited by 85 publications

References 25 publications

An Improved Stability Criterion for Load Frequency Control of Power Systems with Time-Varying Delays

An Improved Stability Criterion for Load Frequency Control of Power Systems with Time-Varying Delays

Delay range‐and‐rate dependent stability criteria for systems with interval time‐varying delay via a quasi‐quadratic convex framework

Robust load frequency control of power systems with two time delays

Contact Info

Product

Resources

About